How do u find the area bounded by the parabola and the latus rectum (1 Viewer)

[Hikari Clover]

Given that x^2=4ay, the latus rectum is y = a

I got 4/3a^2,but the answer is actually twice mine…..

How come…..

is it because when u do x=√(4ay), which is for positive x only?so u have to multiply the answer by 2?

but when we find the area of a circle(use integration),u also do y=√(a^2-x^2),but in this case why dont u multiply the answer by 2?

so confused about it,please help~~

 

[nubix]

You need to push the parabola down or flip it so that the x-axis becomes to the latus rectum.

eg. x²=-4a(y-a)

Put that in terms of y and integrate between -2a and 2a.

EDIT: Or err.. Just integrate y = x²/4a between -2a and 2a. Then subtract that from the rectangle of 4a*a >_<

 

[Mattamz]

alternatively you could consider the:

area = are of rectangle - the area between the parabola and the x-axis

ie: Area = 4a*a - Int(between -2a and 2a)[(x^2)/4a]
= 4a^2 - (4a^2)/3
= (8a^2)/3

 

[morganforrest]

Given that x^2=4ay, the latus rectum is y = a

I got 4/3a^2,but the answer is actually twice mine…..

How come…..

is it because when u do x=√(4ay), which is for positive x only?so u have to multiply the answer by 2?

but when we find the area of a circle(use integration),u also do y=√(a^2-x^2),but in this case why dont u multiply the answer by 2?

so confused about it,please help~~

You multiply the answer by 2 because the integral of root(4ay) only takes into account the positive root. ie everything on the right hand side of the y axis.

So do the integral from 0 - a of root(4ay) . dy and multiply by 2 to take into account both sides of the y axis.

 

[Hikari Clover]

回复: Re: How do u find the area bounded by the parabola and the latus rectum

but when u doing the samething for finding the area of a circle, u dont have to time 2, y????

 

[morganforrest]

Re: 回复: Re: How do u find the area bounded by the parabola and the latus rectum

In your integration of a circle you probably had the limits -a => a in which case you wouldn't multiply by 2.....you can do the same for the parabola...its just easier to use the symmetry and go from 0 to a and multiply by 2

 

[Hikari Clover]

回复: Re: 回复: Re: How do u find the area bounded by the parabola and the latus rectum

ok , i got it ,thx for explaining

 

[Jonny90]

Re: 回复: Re: 回复: Re: How do u find the area bounded by the parabola and the latus rectum

Its SIMPLE!!!!! to find the area or the parabola shit (is that even a f*cking word??) buy a "MAGICALY ENCHANTED DILDO" from the ancient horny nomes of the west side near playboy masion. Once you are there you can find the area of ur latus "RECTUM"

hope this helps..... peace!